78.12.31 problem 5 (g)

Internal problem ID [18318]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 17. The Homogeneous Equation with Constant Coefficients. Problems at page 125
Problem number : 5 (g)
Date solved : Tuesday, January 28, 2025 at 11:46:10 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }+3 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 29

dsolve(x^2*diff(y(x),x$2)+2*x*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} \sin \left (\frac {\sqrt {11}\, \ln \left (x \right )}{2}\right )+c_{2} \cos \left (\frac {\sqrt {11}\, \ln \left (x \right )}{2}\right )}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 42

DSolve[x^2*D[y[x],{x,2}] +2*x*D[y[x],x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 \cos \left (\frac {1}{2} \sqrt {11} \log (x)\right )+c_1 \sin \left (\frac {1}{2} \sqrt {11} \log (x)\right )}{\sqrt {x}} \]